Question

the blocks of masses 2kg in 1 kg respectively are tied to the end of string passing over a light frictionless pulley. the masses are held at the same horizontal level and then released. The distance travelled by the centre of mass in 2 seconds is

Answer 1

the tension is T and the masses travel at a acceleretion after being released.
Now, 2a=2g-T and a=T-1g.
So, a=g/3,
Hence they travel 2*g/3 metre each. Now the distance of centre of mass from the 2 kg mass is (2g/3+2g/3)/3.
So the distance traveled by CoM is 2g/3-(2g/3+2g/3)/3=2g/9.